By J. Amoros

ISBN-10: 0821804987

ISBN-13: 9780821804988

ISBN-10: 1119782112

ISBN-13: 9781119782117

ISBN-10: 2819883613

ISBN-13: 9782819883616

This e-book is an exposition of what's at present identified in regards to the basic teams of compact Kahler manifolds. This category of teams includes all finite teams and is exactly smaller than the category of all finitely presentable teams. For the 1st time ever, this e-book collects jointly the entire effects got within the previous couple of years which target to characterise these endless teams that could come up as basic teams of compact Kahler manifolds. every one of these effects are unfavorable ones, announcing which teams don't come up. they're proved utilizing Hodge conception and its combos with rational homotopy thought, with $L^2$ -cohomology, with the speculation of harmonic maps, and with gauge conception. there are various confident effects to boot, displaying attention-grabbing teams as primary teams of Kahler manifolds, in reality, of gentle advanced projective types. The equipment and methods used shape an enticing mixture of topology, differential and algebraic geometry, and intricate research. The e-book will be helpful to researchers and graduate scholars attracted to any of those parts, and it can be used as a textbook for a sophisticated graduate path. one in every of its extraordinary positive factors is a huge variety of concrete examples. The e-book features a variety of new effects and examples that have no longer seemed somewhere else, in addition to discussions of a few vital open questions within the box

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For any two vector fields X. Y defined on U. K(X, Y) is an endomorphism of C"(U,T*r(X)) and maps C (U, T*°\X)) into itself. 4) (Fx c FY - r,- = Fx) a = (D"(/; ® K(Y, X)) - S(Y,X)®Ill + Fix,n)(a) , rxeC'(U. £ ® A«T*o'(X)) , L denoting identity endomorphism of | and /,, the identity endomorphism of A'P'(i). 4) for q = 1 is just the definition of curvature tensor. 4) is true for a = T**-l(X)) ,

Seeley. Complex powers of an elliptic operator, Proc. Sympos. Pure Math. Vol. 10, Amer. Math. Soc, 1967, 288-307. [ 5 ] E. Vesentini. Lectures on Levi convexity of complex manifolds and cohomology vanishing theorems, Tata Institute of Fundamental Research. Bombay, 1967. TATA I N S T I T U T E F U N D A M E N T A L RESEARCH, BOMBAY 51 Journal of the Indian Math. Soc. 34 (1970) 269-285 CURVATURE AND THE FUNDAMENTAL SOLUTION OF THE HEAT OPERATOR By V. K . P A T O D I [Received December 10, 1970] 1.

Here we shall not go into the details of the proof which are quite straight forward. For any two vector fields X. Y defined on U. K(X, Y) is an endomorphism of C"(U,T*r(X)) and maps C (U, T*°\X)) into itself. 4) (Fx c FY - r,- = Fx) a = (D"(/; ® K(Y, X)) - S(Y,X)®Ill + Fix,n)(a) , rxeC'(U. £ ® A«T*o'(X)) , L denoting identity endomorphism of | and /,, the identity endomorphism of A'P'(i). 4) for q = 1 is just the definition of curvature tensor. 4) is true for a = T**-l(X)) ,

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Fundamental groups of compact Kahler manifolds by J. Amoros


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